Abstract:We prove that the essential range of the gradient of planar Lipschitz maps has a connected
rank-one convex hull. As a corollary, in combination with the results in Faraco, D., and Székelyhidi, Jr., L.:
Tartar's conjecture and localization of the quasiconvex hull in
. Preprint, MPI-MIS, 2006.
we obtain
a complete characterization of incompatible sets of gradients for planar maps in terms of rank-one convexity.